Abstract: Density functional calculations are performed for ground He2s$^2$$^1$S$^e$, and three metastable bound excited states, 1s2s2p$^2$ $^5$P$^e$,1s2p$^3$ $^5$S$^o$, 1s2s2p3p $^5$P$^e$ of Li$^-$ and He2s2p$^2$ $^4$P$^e$,He2p$^3$ $^4$S$^o$, 1s2s2p$^3$ $^6$S$^o$ of Be$^-$ each. Thework-function-based exchange potential is used, while the correlation effectsare included by employing the Lee-Yang-Parr potential. The relevantnonrelativistic KS equation is solved by means of a generalized pseudospectraldiscretization scheme offering nonuniform and optimal spatial grid. Computedtotal energies, radial densities, selected density moments, as well as twotransition wavelengths 1s2s2p$^2$ $^5$P$^e \to$1s2p$^3$ $^5$S$^o$ of Li$^-$,He2s2p$^2$ $^4$P$^e \to$ He2p$^3$ $^4$S$^o$ of Be$^-$ show reasonably goodagreement with the available theoretical and experimental data. The termenergies show an absolute deviation of 0.007-0.171% with the largest deviationbeing observed for the even-parity $^5$P state of Li$^-$. The transitionwavelengths of Li$^-$, Be$^-$ are calculated within 0.891 and 0.438% of theexperimental values. This offers a simple practical route towards accuratereliable calculation of excited states of anions within density functionaltheory.